Consider the transformation A created by projecting a vector x onto the line shown in Figure E6.3. An example of the transformation is shown in the figure. i. Using Eq. (6.6), find the matrix...

Consider the transformation A created by projecting a vector x onto the line shown in Figure E6.3. An example of the transformation is shown in the figure.

i. Using Eq. (6.6), find the matrix representation of this transformation relative to the standard basis set

ii. Using your answer to part i, find the matrix representation of this transformation relative to the basis setshown in Figure E6.3.

iii. What are the eigenvalues and eigenvectors of this transformation? Sketch the eigenvectors and their transformations.